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Because I'm sort of in the same position (but having already started a post-grad fellowship), I might be able to point out some issues.

Will your employer be flexible and understanding about the job search? If you get an interview, it would mean flying to California. This might get int he way of your schedule, but if your job search is near the end of your fellowship/job, then it might not be a big deal.

The big problem is networking. You can't really network while you're out of state, and networking is pretty useful in finding a job post-graduation. Maybe it can be done but who knows.

Also, hopefully you are from CA. Employers might wonder why you are working out of state, though your CA bar admission might help alleviate any concerns.

Overall, no one can give you a straight and easy answer. The post-grad search is pretty unpredictable. Pretty much anything can happen, and things might help (networking, having strong grades/ties, etc.) but it's not rigid like OCI. However, these are all factors you need to weigh to see if you're making the right decision.